Methods and apparatus for assembling rotatable machines

Abstract

A processor-implemented method of assembling a rotatable machine is provided. The machine includes a plurality of blades that extend radially outwardly from a rotor. The method includes determining a geometric parameter for each blade in a row of blades that is relative to a ratio, R of an inlet area and an outlet area of a predetermined volume defined between each pair of blades, determining an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades, and iteratively remapping the sequence of the blades to facilitate reducing a moment weight vector sum of the rotor to a value that is less than a predetermined value.

1. A method of assembling a rotatable machine that includes a plurality of blades that extend radially outwardly from a rotor, said method comprising:
 determining, using a computer a geometric parameter for each blade in a row of blades that is relative to a ratio, R of an inlet area and an outlet area of a predetermined volume between each pair of blades; 
 determining, using the computer R using the determined geometric parameter; 
 determining an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades; 
 selecting, using the computer, each blade placement in a subsequent map based on the blade's contribution to a variation of R between each blade and adjacent blade in a pair of blades in the row of blades; 
 iteratively swapping and remapping the sequence of the blades, using the computer perform blade mapping, to facilitate reducing a moment weight vector sum of the rotor to a value that is less than a predetermined value; 
 outputting using the computer, a final blade map describing a location on the rotor to install each blade, the final blade map based on an endpoint of the remapping; and 
 installing the blades on the rotor based on the final blade map. 
 
     
     
       2. A method in accordance with  claim 1  further comprising categorizing each blade based on a determined contribution of the blade to R associated with the blade. 
     
     
       3. A method in accordance with  claim 1  wherein determining an initial sequence map for the row of blades comprises determining an initial sequence map for the row of blades that facilitates minimizing at least one of a summation of the differences between inlet areas of circumferentially adjacent volumes, a summation of the differences between exit areas of circumferentially adjacent volumes, a summation of the differences between circumferentially adjacent volumes, a summation of the root sum squared values of the differences between inlet areas of circumferentially adjacent volumes and the difference between respective exit areas of circumferentially adjacent volumes, and a summation of the difference between the ratio of exit area to inlet area of circumferentially adjacent volumes for each blade. 
     
     
       4. A method in accordance with  claim 1  wherein iteratively remapping the sequence of the blades comprises exchanging a first blade located in a first map position with a second blade, located in a second map position, of a same category as the first blade. 
     
     
       5. A method in accordance with  claim 1  wherein iteratively remapping the sequence of the blades further comprises determining a remapping sequence that facilitates minimizing a number of blade exchanges used to facilitate reducing the moment weight vector sum of the rotor to a value less than a predetermined limit. 
     
     
       6. A method in accordance with  claim 1  wherein determining a geometric parameter for each blade in a row of blades comprises receiving a geometric parameter for at least one of a sonic, a transonic, and a supersonic portion for each blade in the row of blades. 
     
     
       7. A rotor assembly comprising:
 a disk comprising a plurality of circumferentially-spaced blade root slots defined therein; and 
 a plurality of blades comprising geometric differences with respect to each other, each said blade comprising a root, a tip, and an airfoil extending therebetween, each said blade positioned within a pre-determined slot based on a blade map generated to minimize multiple pure tone noise, said blade map generated by a computer system configured to:
 determine a geometric parameter for each blade in a row of blades that is relative to a ratio, R of an inlet area and an outlet area of a predetermined volume defined between each pair of blades; 
 determine R using the determined geometric parameter; 
 determine an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades; 
 select each blade placement in each subsequent map based on the blade's contribution to a variation of R between each of said plurality of blades in the row of blades; 
 iteratively swap and remap the sequence of the blades to facilitate reducing a moment weight vector sum of the rotor to a value that is less than a predetermined value; and 
 output the final blade map, 
 
 wherein, in the rotor assembly, when fully assembled, said plurality of blades are sequenced circumferentially in said disk such that a difference of R between a first adjacent pair of said plurality of blades is less than a determined difference of R between a second adjacent pair of said plurality of blades, said first and second pairs of blades being adjacent in the disk with respect to each other. 
 
     
     
       8. A rotor assembly in accordance with  claim 7  wherein said computer system is further configured to categorize each blade based on a determined contribution of the blade to R associated with the blade. 
     
     
       9. A rotor assembly in accordance with  claim 7  wherein said plurality of blades are composite fan blades. 
     
     
       10. A rotor assembly in accordance with  claim 7  wherein said computer system is further configured to determine a ratio of an inlet area to an exit area that are defined between each pair of adjacent blades. 
     
     
       11. A rotor assembly in accordance with  claim 7  wherein said computer system is further configured to determine an initial sequence map for the row of blades that facilitates minimizing at least one of a summation of the differences between inlet areas of circumferentially adjacent volumes, a summation of the differences between exit areas of circumferentially adjacent volumes, a summation of the differences between circumferentially adjacent volumes, a summation of the root sum squared values of the differences between inlet areas of circumferentially adjacent volumes and the difference between respective exit areas of circumferentially adjacent volumes, and a summation of the difference between the ratio of exit area to inlet area of circumferentially adjacent volumes for each blade. 
     
     
       12. A rotor assembly in accordance with  claim 7  wherein said computer system is further configured to:
 exchange a first blade located in a first map position with a second blade, located in a second map position, of a same category as the first blade; and 
 determine a moment weight vector sum of the rotor with the first blade in the second map position and the second blade in the first map position. 
 
     
     
       13. A rotor assembly in accordance with  claim 12  wherein said computer system is further configured to compare the determined moment weight vector sum of the rotor to the predetermined value. 
     
     
       14. A non-transitory computer readable medium on which is recorded computer executable instructions for use in facilitating reducing multiple pure tone noise and imbalance in a bladed rotor, said executable instructions when executed by a processor perform a process that:
 prompts a user to select a plurality of blades for installation on the bladed rotor; 
 determines a geometric parameter for each blade in a row of blades that is relative to a ratio, R of an inlet area and an outlet area of a predetermined volume defined between each pair of adjacent blades; 
 determines R using the determined geometric parameter; 
 determines an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades; 
 selects each placement in a subsequent map based on a first blade's contribution to a variation of R between each blade and adjacent blade in a pair of blades in the row of blades; 
 iteratively swaps and remaps the sequence of the blades to facilitate reducing a moment weight vector sum of the rotor to a value that is less than a predetermined value; and 
 outputs a final blade map describing a location on the rotor to install each blade, the final blade map based on an endpoint of the remapping. 
 
     
     
       15. A computer readable medium in accordance with  claim 14  wherein said executable instructions when executed by a processor perform a process that categorizes each blade based on a determined contribution of the blade to R associated with the blade. 
     
     
       16. A computer readable medium in accordance with  claim 14  wherein said executable instructions when executed by a processor perform a process that determines an initial sequence map for the row of blades that facilitates minimizing at least one of a summation of the differences between inlet areas of circumferentially adjacent volumes, a summation of the differences between exit areas of circumferentially adjacent volumes, a summation of the differences between circumferentially adjacent volumes, a summation of the root sum squared values of the differences between inlet areas of circumferentially adjacent volumes and the difference between respective exit areas of circumferentially adjacent volumes, and a summation of the difference between the ratio of exit area to inlet area of circumferentially adjacent volumes for each blade. 
     
     
       17. A computer readable medium in accordance with  claim 14  wherein said executable instructions when executed by a processor perform a process that generates a blade sequence map that exchanges a first blade located in a first map position with a second blade, located in a second map position, of a same category as the first blade. 
     
     
       18. A computer readable medium in accordance with  claim 14  wherein said executable instructions when executed by a processor perform a process that determines a blade remapping sequence that facilitates minimizing a number of blade swaps that reduces the moment weight vector sum of the rotor to a value less than a predetermined limit. 
     
     
       19. A computer-implemented method of assembling an aircraft gas turbine engine that includes a rotor assembly having a plurality of composite blades that extend radially outwardly from a plurality of circumferentially-spaced slots, said method comprising:
 determining a geometric parameter for each blade in a row of blades that is relative to a ratio, R, of an inlet area and an outlet area of a predetermined volume defined between each pair of adjacent blades; 
 determining ratio R using the determined geometric parameter; 
 categorizing each blade based on a determined contribution of the blade to R associated with the blade; 
 determining an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades; 
 selecting each blade placement in a subsequent map based on the blade's contribution to a variation of R between each blade and adjacent blade in a pair of blades in the row of blades; 
 iteratively swapping and remapping the sequence of the blades, using a computer including a processor programmable with instructions to perform blade mapping, to reduce a moment weight vector sum of the rotor to a value that is less than a predetermined value; 
 exchanging a first blade located in a first map position with a second blade, located in a second map position, of a same category as the first blade; 
 outputting, using the computer, a final blade map that describes a location on the rotor to install each blade, wherein the final blade map is based on an endpoint of the remapping; and 
 installing the blades on the rotor based on the final blade map, wherein, in the rotor assembly, when fully assembled, said plurality of blades are sequenced circumferentially in said disk such that a difference of R between a first adjacent pair of said plurality of blades is less than a determined difference of R between a second adjacent pair of said plurality of blades, said first and second pairs of blades being adjacent with respect to each other. 
 
     
     
       20. A method in accordance with  claim 19  wherein determining an initial sequence map for the row of blades that facilitates minimizing a difference of R between circumferentially adjacent pairs of blades comprises determining an initial sequence map for the row of blades that minimizes at least one of a summation of the differences between inlet areas of circumferentially adjacent volumes, a summation of the differences between exit areas of circumferentially adjacent volumes, a summation of the differences between circumferentially adjacent volumes, a summation of the root sum squared values of the differences between inlet areas of circumferentially adjacent volumes and the difference between respective exit areas of circumferentially adjacent volumes, and a summation of the difference between the ratio of exit area to inlet area of circumferentially adjacent volumes for each blade.